Is there a formula for the present value of a stream of payments that increases by a specific amount at the beginning of each new year? For example, Mr. Smith gets \$100 every 2 weeks but at the beginning of each new year the bi-weekly payment goes up \$15 so for the new year he gets \$115 every 2 weeks, and the next year his bi-weekly payments goes up to \$130 and so on.....

So far, the formulas I found only calculate present value of an increasing annuity using a compounding factor.

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Quote:

Originally Posted by cb123

Is there a formula for the present value of a stream of payments that increases by a specific amount at the beginning of each new year? For example, Mr. Smith gets \$100 every 2 weeks but at the beginning of each new year the bi-weekly payment goes up \$15 so for the new year he gets \$115 every 2 weeks, and the next year his bi-weekly payments goes up to \$130 and so on.....

So far, the formulas I found only calculate present value of an increasing annuity using a compounding factor.

In your example, G is the annual increase, i is the discount factor?, c is the discount factor divided by the number of periods(p)? Is that correct?

Code:

A=100 : initial payment at the end of each two weeks
G=15 : annual increase
i : annual nominal interest rate such as 12%
c : interest compounding frequency such as 1/26 biweekly then periodic rate is i*c = 0.12/26 = 0.46% is the biweekly rate
p : payment period, in this case bi-weekly = 2/52 = 1/26
n : n is the number of years

As for the formula, there are couple of issues I will address a bit later

Firstly formula is used when n is complete number of years, I will later fix this to include years with fractional part

For complete number of periods in a year, the following is a general case formula to find present value of an ordinary annuity (end of period payments) that have payments which may increase or decrease by a money amount per period